Distinct Properties of Vortex Bound States Driven by Temperature

TL;DR

This study explores how vortex bound states behave in the quantum limit, revealing temperature-dependent deviations from classical models and unique local density of states features, advancing understanding of vortex physics.

Contribution

It provides a self-consistent analysis of vortex bound states in the quantum limit, highlighting temperature effects and deviations from analytical energy predictions.

Findings

Energy ratios deviate from classical predictions at low temperatures.

Local density of states shows Friedel-like oscillations in the quantum limit.

Thermal effects smooth out quantum features above a certain temperature.

Abstract

We investigate the behavior of vortex bound states in the quantum limit by self-consistently solving the Bogoliubov-de Gennes equation. We find that the energies of the vortex bound states deviates from the analytical result $E_\mu=\mu\Delta^2/E_F$ with the half-integer angular momentum $\mu$ in the extreme quantum limit. Specifically, the energy ratio for the first three orders is more close to $1:2:3$ instead of $1:3:5$ at extremely low temperature. The local density of states reveals an Friedel-like behavior associated with that of the pair potential in the extreme quantum limit, which will be smoothed out by thermal effect above a certain temperature even the quantum limit condition, namely $T/T_c<\Delta/E_F$ is still satisfied. Our studies show that the vortex bound states can exhibit very distinct features in different temperature regimes, which provides a comprehensive understanding and should stimulate more experimental efforts for verifications.